I was thinking about the Hall Effect Thrusters and how they are able to produce thrust. There's something that I don't understand: when the hollow cathodes emit electrons to neutralize the flow at the exit, there are some electrons going back to the exit of the channel. On the other hand, there are some electrons trapped in the magnetic field (radial direction) along the channel and it works as a magnetic resistance. Do you know if there's an accumulation of electrons over time in the magnetic field? If yes, can problems appear when ionizing the fluid?
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$\begingroup$ since same-sign charges repel, any accumulation of same-sign charges not accompanied by corresponding accumulation of the opposite sign charges is dissipating itself pretty quickly on its own. $\endgroup$– SF.Commented Jun 14, 2016 at 9:28
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$\begingroup$ @Nathan Tuggy, therefore there's no accumulation of electrons in the magnetic field because of the continuously dissipation between the positive-negative charges when producing thrust? The electrons emitted by the hollow cathode from outside are being atracted to the magnetic field, there are some electrons that go towards the anode. Are they entering another time into the cathode? It's like a close circuit? $\endgroup$– Panri93Commented Jun 14, 2016 at 9:43
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$\begingroup$ XaviPars, I think you meant to reply to @SF., not me. $\endgroup$– Nathan TuggyCommented Jun 14, 2016 at 17:02
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$\begingroup$ @XaviPars: I don't know how exactly Hall thrusters work. I just know that accumulation of any meaningful amount of single-sign charge is about impossible by all known technical means, as the repulsion force becomes enormous really fast. Any meaningful charges are storable only as differential - simultaneously positive and negative charge, for a total sum oscillating around zero. You just can't store a Coulomb of electrons without placing them really close to a corresponding amount of positive ions. And we're not even talking about intentional storage here, just accidental accumulation. $\endgroup$– SF.Commented Jun 14, 2016 at 17:25
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It is precisely the "accumulation" of electrons that makes the Hall thruster work. Basically you need to have enough electrons trapped in your $\mathrm{E}\times\mathrm{B}$ field, drifting in the azimuthal direction (along the channel) to ionize your gas and generate the ions that are in turn accelerated to generate thrust. You can see more details in Goebel's book but I will summarize the operation of the thruster below.
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Here is a simplified description of its operation:
- When the thruster is off, gas is injected through its anode and fill the channel. A positive voltage is applied to the anode, which creates an electric field in the $z$ direction.
- The cathode is then turned on and its electrons flow towards the anode due to the potential difference.
- When electrons enter the channel they suffer the influence of two different fields, an axial electric field $E_z$, and a radial magnetic field $B_r$. This configuration makes the electron orbit and drift in a direction perpendicular to $E_z$ and $B_r$ ($\theta$ or azimuthal direction), with an average drift velocity of $v_d = E_z / B_r$. The radius of the orbit is given by the energy of the electron as it enters the cross field configuration. This is shown in the figure.
- The drifting electrons create the so-called azimuthal current which starts to ionize the gas and produce ions, creating a plasma.
- Ions are accelerated outwards due to the electric field created inside the plasma and electrons are slowly lost to the anode and walls. Other electrons emitted by the cathode also flow away with the ions, neutralizing the ion beam so that charge balance is guaranteed.
The amount of electrons accumulated in the discharge depends on several factors. However, there is a saturation point like in a reservoir, where there are enough electrons in the discharge so that the net potential created by ions and electrons in the channel attracts only a current enough to balance the amount of electrons that are lost to the anode.
In an "ideal" Hall thruster almost no electron would flow to the anode. In the beginning people thought the amount of electrons lost would be given by the magnetic cross field mobility ($\mu = \frac{mv_\perp^2}{2B} $). However it was later observed that the electrons loss was much higher than predicted. This so-called anomalous electron transport is mainly caused by turbulence and instabilities and is still an active theme of research.
